sksurv.svm.MinlipSurvivalAnalysis

class sksurv.svm.MinlipSurvivalAnalysis(solver='cvxpy', alpha=1.0, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, pairs='nearest', verbose=False, timeit=None, max_iter=None)

Survival model related to survival SVM, using a minimal Lipschitz smoothness strategy instead of a maximal margin strategy.

\[ \begin{align}\begin{aligned}\begin{split}\min_{\mathbf{w}}\quad \frac{1}{2} \lVert \mathbf{w} \rVert_2^2 + \gamma \sum_{i = 1}^n \xi_i \\ \text{subject to}\quad \mathbf{w}^\top \mathbf{x}_i - \mathbf{w}^\top \mathbf{x}_j \geq y_i - y_j - \xi_i,\quad \forall (i, j) \in \mathcal{P}_\text{1-NN}, \\ \xi_i \geq 0,\quad \forall i = 1,\dots,n.\end{split}\\\mathcal{P}_\text{1-NN} = \{ (i, j) \mid y_i > y_j \land \delta_j = 1 \land \nexists k : y_i > y_k > y_j \land \delta_k = 1 \}_{i,j=1}^n.\end{aligned}\end{align} \]
Parameters:
solver : “cvxpy” | “cvxopt”, optional, default: cvxpy

Which quadratic program solver to use.

alpha : float, positive, default: 1

Weight of penalizing the hinge loss in the objective function.

kernel : “linear” | “poly” | “rbf” | “sigmoid” | “cosine” | “precomputed”

Kernel. Default: “linear”

gamma : float, optional

Kernel coefficient for rbf and poly kernels. Default: 1/n_features. Ignored by other kernels.

degree : int, default: 3

Degree for poly kernels. Ignored by other kernels.

coef0 : float, optional

Independent term in poly and sigmoid kernels. Ignored by other kernels.

kernel_params : mapping of string to any, optional

Parameters (keyword arguments) and values for kernel passed as call

pairs : “all” | “nearest” | “next”, optional, default: “nearest”

Which constraints to use in the optimization problem.

  • all: Use all comparable pairs. Scales quadratic in number of samples (cf. sksurv.svm.HingeLossSurvivalSVM).
  • nearest: Only considers comparable pairs \((i, j)\) where \(j\) is the uncensored sample with highest survival time smaller than \(y_i\). Scales linear in number of samples.
  • next: Only compare against direct nearest neighbor according to observed time, disregarding its censoring status. Scales linear in number of samples.
verbose : bool, default: False

Enable verbose output of solver

timeit : False or int

If non-zero value is provided the time it takes for optimization is measured. The given number of repetitions are performed. Results can be accessed from the timings_ attribute.

max_iter : int, optional

Maximum number of iterations to perform. By default use solver’s default value.

References

[1]Van Belle, V., Pelckmans, K., Suykens, J. A. K., and Van Huffel, S. Learning transformation models for ranking and survival analysis. The Journal of Machine Learning Research, 12, 819-862. 2011
Attributes:
X_fit_ : ndarray

Training data.

coef_ : ndarray, shape = (n_samples,)

Coefficients of the features in the decision function.

__init__(solver='cvxpy', alpha=1.0, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, pairs='nearest', verbose=False, timeit=None, max_iter=None)

Methods

__init__([solver, alpha, kernel, gamma, …])
fit(X, y) Build a MINLIP survival model from training data.
predict(X) Predict risk score of experiencing an event.
score(X, y)
fit(X, y)

Build a MINLIP survival model from training data.

Parameters:
X : array-like, shape = (n_samples, n_features)

Data matrix.

y : structured array, shape = (n_samples,)

A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.

Returns:
self
predict(X)

Predict risk score of experiencing an event.

Higher scores indicate shorter survival (high risk), lower scores longer survival (low risk).

Parameters:
X : array-like, shape = (n_samples, n_features)

The input samples.

Returns:
y : ndarray, shape = (n_samples,)

Predicted risk.